Variation · Form 5
Variation: Key Terms
The key Variation terms you need for SPM Mathematics, defined plainly in English, Malay and Chinese.
- Direct variation A relationship where one quantity increases as the other increases, written y = kx.
- Inverse variation A relationship where one quantity decreases as the other increases, written y = k/x.
- Joint variation A relationship where one quantity varies with two or more others at once.
- Direct variation A relationship where one quantity increases at a constant rate as another increases, y = kx.
- Inverse variation A relationship where one quantity decreases as another increases so their product is constant, y = k/x.
- Constant of variation The fixed number k linking the quantities in a variation relationship.
Term pairs students mix up
- Direct variation vs inverse variation, direct keeps the RATIO y/x constant (y = kx); inverse keeps the PRODUCT xy constant (y = k/x).
- Joint variation vs combined variation, joint variation multiplies everything (y = kxz); combined variation mixes a multiply and a divide (y = kx/z).
- Constant of variation vs the variables, k is fixed for the whole relationship, while x, y and z change. Find k once, then reuse it everywhere.
- 'Varies as' vs 'is equal to' 'varies as' is the ∝ stage with no number yet; you only reach '=' after you introduce and calculate k.
How these terms appear in real SPM questions
SPM questions hide the equation inside trigger words. 'y varies directly as x' or 'y is proportional to x' → y = kx.
'y varies inversely as x' → y = k/x. 'y varies directly as x and inversely as z' → y = kx/z.
'y is proportional to the square of x' → y = kx². 'y varies jointly as x and z' → y = kxz.
Read it like this: 'directly' or 'proportional' means multiply, 'inversely' means divide, 'square/cube/square root of' puts that power on its own variable, and 'jointly' means a product. Translate the whole sentence into symbols before you touch a single number.
Source:DSKP KSSM Mathematics Form 4 and 5 (Versi English)
Frequently asked questions
Does 'varies as' mean the same as 'is proportional to'?
Yes, they are identical in this chapter. 'y varies as x', 'y is proportional to x' and 'y ∝ x' all lead to y = kx.
Different SPM questions use different wording for the same idea, so treat all three phrasings as the same instruction: form a proportionality and introduce k.
Can I write the ∝ symbol in my answer, or must I use =?
You may and should write ∝ as your first line, it shows you have read the relationship. But you cannot calculate with ∝; the next line must replace it with = k to give a usable equation.
Marks for the final value depend on that equation, so never leave the answer at the ∝ stage.
Is 'constant of variation' the same as 'constant of proportionality'?
Yes. Both names refer to k, the fixed number linking the quantities.
'Constant of variation' is the wording the SPM syllabus favours, but 'constant of proportionality' means exactly the same thing. Whatever the question calls it, it is the k you find first and reuse throughout the problem.